Moments of Sunlight Pathlength in Water and Aerosol Clouds from O$_2$ Spectroscopy: Exploitable Parameter Sensitivities.

The last IPCC assessment states that clouds and aerosols remain a challenge in climate prediction with Global Climate Models. Therefore, NASA's 2017 Decadal Survey has made them, along with convection and precipitation, a priority target for future missions under the ACCP banner, now Atmospheric Observing System. Atmospheric science is now more than ever driving renewal in remote sensing to probe clouds and aerosols more accurately and with improved sampling. Here, we bring new results that support Differential Optical Absorption Spectroscopy (DOAS) using oxygen absorption features in the visible/near-IR spectrum. With known concentration and cross-section, the remaining unknown in O$_2$ DOAS is the path the light followed through the absorbing gas. In presence of scattering by cloud or aerosol particles, that path is broken at each interaction. Cumulative pathlength through the gas is a random variable, and its probability distribution function (PDF) will contain desirable information about the clouds or aerosols. Here, we compute statistical moments of the that PDF, showing that mean and variance convey different pieces of information, namely, size and opacity of the medium. We also extend the connection between geometric thickness and mean pathlength in presence of absorption by the scattering particles. We view pathlength moments as intermediate products that can be obtained from O$_2$ spectroscopy, and describe an algorithm to do that. In turn, these moments yield cloud or aerosol profile parameters of interest: layer geometric and optical thicknesses. One normally thinks about active sensors, radars and lidars, for such atmospheric profiling. Here, the profile is parameterized and representative of a horizontal average determined by multiple scattering. However, there are advantages in passive vs active instrumentation, starting with the possibility of imaging over a large swath.